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<p><dfn class="terminology">Summary</dfn>Following five statements are equivalent, regarding <span class="process-math">\(y^{\prime \prime}+p(x) y^{\prime}+q(x)=0\)</span> with two solutions <span class="process-math">\(y_1\)</span> and <span class="process-math">\(y_2\text{:}\)</span>1. <span class="process-math">\(W(y_1, y_2)|_{x=x_0} \neq 0\text{;}\)</span>2. <span class="process-math">\(W(y_1, y_2) \neq 0\)</span> for all <span class="process-math">\(x\text{;}\)</span>3. <span class="process-math">\(y_1\)</span> and <span class="process-math">\(y_2\)</span> are linear independent.4. <span class="process-math">\(y_1\)</span> and <span class="process-math">\(y_2\)</span> are a fundamental set of solutions;5. <span class="process-math">\(C_1 y_1+C_2 y_2\)</span> is the general solution;</p>
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